%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:46:55 EDT 2022 % Result : Theorem 36.48s 10.70s % Output : Proof 46.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU142+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 21:04:53 EDT 2022 % 0.13/0.34 % CPUTime : % 0.62/0.64 ____ _ % 0.62/0.64 ___ / __ \_____(_)___ ________ __________ % 0.62/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.62/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.62/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.62/0.64 % 0.62/0.64 A Theorem Prover for First-Order Logic % 0.62/0.64 (ePrincess v.1.0) % 0.62/0.64 % 0.62/0.64 (c) Philipp Rümmer, 2009-2015 % 0.62/0.64 (c) Peter Backeman, 2014-2015 % 0.62/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.64 Bug reports to peter@backeman.se % 0.62/0.64 % 0.62/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.64 % 0.62/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.80/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.67/1.00 Prover 0: Preprocessing ... % 2.75/1.33 Prover 0: Warning: ignoring some quantifiers % 3.00/1.36 Prover 0: Constructing countermodel ... % 4.76/1.76 Prover 0: gave up % 4.76/1.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.76/1.81 Prover 1: Preprocessing ... % 5.24/1.94 Prover 1: Warning: ignoring some quantifiers % 5.65/1.94 Prover 1: Constructing countermodel ... % 5.83/2.00 Prover 1: gave up % 5.83/2.00 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.83/2.04 Prover 2: Preprocessing ... % 6.64/2.20 Prover 2: Warning: ignoring some quantifiers % 6.64/2.21 Prover 2: Constructing countermodel ... % 7.04/2.29 Prover 2: gave up % 7.04/2.29 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.22/2.32 Prover 3: Preprocessing ... % 7.37/2.36 Prover 3: Warning: ignoring some quantifiers % 7.37/2.36 Prover 3: Constructing countermodel ... % 8.05/2.54 Prover 3: gave up % 8.05/2.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 8.37/2.57 Prover 4: Preprocessing ... % 8.70/2.70 Prover 4: Warning: ignoring some quantifiers % 8.70/2.70 Prover 4: Constructing countermodel ... % 12.80/3.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 13.20/3.74 Prover 5: Preprocessing ... % 13.61/3.88 Prover 5: Warning: ignoring some quantifiers % 13.99/3.88 Prover 5: Constructing countermodel ... % 14.16/3.96 Prover 5: gave up % 14.16/3.96 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 14.16/4.01 Prover 6: Preprocessing ... % 14.90/4.12 Prover 6: Warning: ignoring some quantifiers % 14.90/4.12 Prover 6: Constructing countermodel ... % 15.24/4.18 Prover 6: gave up % 15.24/4.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 15.37/4.20 Prover 7: Preprocessing ... % 15.48/4.24 Prover 7: Proving ... % 36.48/10.69 Prover 7: proved (6515ms) % 36.48/10.69 Prover 4: stopped % 36.48/10.70 % 36.48/10.70 % SZS status Theorem for theBenchmark % 36.48/10.70 % 36.48/10.70 Generating proof ... found it (size 45) % 46.01/15.24 % 46.01/15.24 % SZS output start Proof for theBenchmark % 46.01/15.24 Assumed formulas after preprocessing and simplification: % 46.01/15.24 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (set_difference(v2, v3) = v5) | ~ (set_difference(v1, v3) = v4) | ~ subset(v1, v2) | subset(v4, v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v1, v3) = v4) | ~ subset(v1, v2) | subset(v4, v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v1, v3) = v4) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_union2(v4, v3) = v2) | ~ (set_union2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (unordered_pair(v4, v3) = v2) | ~ (unordered_pair(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (set_union2(v1, v2) = v3) | set_difference(v1, v2) = v4) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v1, v3) = v4) | set_union2(v1, v2) = v4) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (set_difference(v1, v2) = v3) | set_intersection2(v1, v2) = v4) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | ~ subset(v1, v3) | ~ subset(v1, v2) | subset(v1, v4)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v3) = v4) | ~ subset(v3, v2) | ~ subset(v1, v2) | subset(v4, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_union2(v1, v2) = v3) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v2) = v3) | ~ disjoint(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_intersection2(v1, v2) = v3) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ disjoint(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | subset(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) & ~ in(v5, v2)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) & ~ in(v4, v2))) & ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ disjoint(v1, v2) | ! [v4] : ~ in(v4, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | disjoint(v1, v2) | ? [v4] : in(v4, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | subset(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v2) | ~ in(v5, v1)) & (in(v5, v4) | (in(v5, v2) & in(v5, v1)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v2) & in(v4, v1))) & ! [v4] : ( ~ in(v4, v2) | ~ in(v4, v1) | in(v4, v3)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v2, v1) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | set_union2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | subset(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ( ~ in(v5, v2) & ~ in(v5, v1))) & (in(v5, v4) | in(v5, v2) | in(v5, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | in(v4, v2) | in(v4, v1)) & ! [v4] : (in(v4, v3) | ( ~ in(v4, v2) & ~ in(v4, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | unordered_pair(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : ((v5 = v2 | v5 = v1 | in(v5, v4)) & ( ~ in(v5, v4) | ( ~ (v5 = v2) & ~ (v5 = v1)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ( ! [v4] : (v4 = v2 | v4 = v1 | ~ in(v4, v3)) & ! [v4] : (in(v4, v3) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ disjoint(v2, v3) | ~ subset(v1, v2) | disjoint(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ subset(v2, v3) | ~ subset(v1, v2) | subset(v1, v3)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v1, v2) | proper_subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ~ in(v3, v1)) & (in(v3, v2) | in(v3, v1)))) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v1, v0) = v2)) & ! [v1] : ! [v2] : ( ~ (set_difference(v1, v2) = v1) | disjoint(v1, v2)) & ! [v1] : ! [v2] : ( ~ (set_difference(v1, v2) = v0) | subset(v1, v2)) & ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ (v4 = v1) | ~ in(v1, v3)) & (v4 = v1 | in(v4, v3))))) & ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | (in(v1, v2) & ! [v3] : (v3 = v1 | ~ in(v3, v2)))) & ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v2) = v0) | disjoint(v1, v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | disjoint(v2, v1)) & ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1))) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ proper_subset(v2, v1)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ proper_subset(v2, v1) | ~ proper_subset(v1, v2)) & ! [v1] : ! [v2] : ( ~ proper_subset(v1, v2) | ( ~ (v2 = v1) & subset(v1, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (disjoint(v1, v2) | ? [v3] : (in(v3, v2) & in(v3, v1))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : (v1 = v0 | ~ subset(v1, v0)) & ! [v1] : (v1 = v0 | ? [v2] : in(v2, v1)) & ! [v1] : ~ proper_subset(v1, v1) & ! [v1] : ~ in(v1, v0) & ! [v1] : subset(v1, v1) & ! [v1] : subset(v0, v1) & ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & singleton(v1) = v3 & unordered_pair(v1, v1) = v2) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1)) % 46.44/15.28 | Instantiating (0) with all_0_0_0 yields: % 46.44/15.28 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ! [v3] : ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = all_0_0_0) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | ! [v2] : ( ~ in(v2, v1) | ~ in(v2, v0))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | ( ~ (v1 = v0) & subset(v0, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0)) & ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, all_0_0_0) & ! [v0] : subset(v0, v0) & ! [v0] : subset(all_0_0_0, v0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 46.56/15.30 | % 46.56/15.30 | Applying alpha-rule on (1) yields: % 46.56/15.30 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 46.56/15.30 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 46.56/15.30 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 46.56/15.30 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) % 46.56/15.30 | (6) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 46.56/15.30 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 46.56/15.30 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 46.56/15.30 | (9) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) % 46.56/15.30 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 46.56/15.30 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 46.56/15.30 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) % 46.56/15.30 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 46.56/15.30 | (14) ! [v0] : subset(v0, v0) % 46.56/15.30 | (15) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) % 46.56/15.30 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 46.56/15.30 | (17) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 46.56/15.30 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0))))) % 46.56/15.30 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 46.56/15.30 | (20) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = all_0_0_0) | subset(v0, v1)) % 46.56/15.30 | (21) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1)) % 46.56/15.30 | (22) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 46.56/15.30 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 46.56/15.30 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ! [v3] : ~ in(v3, v2)) % 46.56/15.30 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0)))))) % 46.56/15.31 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 46.56/15.31 | (27) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) % 46.56/15.31 | (28) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | ( ~ (v1 = v0) & subset(v0, v1))) % 46.56/15.31 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) % 46.56/15.31 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 46.56/15.31 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 46.56/15.31 | (32) ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0)) % 46.56/15.31 | (33) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 46.56/15.31 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 46.56/15.31 | (35) ! [v0] : ~ proper_subset(v0, v0) % 46.56/15.31 | (36) empty(all_0_0_0) % 46.56/15.31 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 46.56/15.31 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 46.56/15.31 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) % 46.56/15.31 | (40) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 46.56/15.31 | (41) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 46.56/15.31 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 46.56/15.31 | (43) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1) % 46.56/15.31 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 46.56/15.31 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 46.56/15.31 | (46) ? [v0] : empty(v0) % 46.56/15.31 | (47) ! [v0] : ! [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 46.56/15.31 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 46.56/15.31 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 46.56/15.31 | (50) ! [v0] : ~ in(v0, all_0_0_0) % 46.56/15.31 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 46.56/15.31 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 46.56/15.31 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 46.56/15.31 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) % 46.56/15.31 | (55) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) % 46.56/15.31 | (56) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 46.56/15.31 | (57) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 46.56/15.31 | (58) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 46.56/15.31 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 46.56/15.31 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) % 46.56/15.31 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 46.56/15.31 | (62) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 46.56/15.31 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 46.56/15.31 | (64) ! [v0] : subset(all_0_0_0, v0) % 46.56/15.31 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 46.56/15.32 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 46.56/15.32 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) % 46.56/15.32 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) % 46.56/15.32 | (69) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) % 46.56/15.32 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 46.56/15.32 | (71) ? [v0] : ~ empty(v0) % 46.56/15.32 | (72) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | ! [v2] : ( ~ in(v2, v1) | ~ in(v2, v0))) % 46.56/15.32 | (73) ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0)) % 46.56/15.32 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 46.56/15.32 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 46.56/15.32 | % 46.56/15.32 | Instantiating (43) with all_7_0_3, all_7_1_4, all_7_2_5 yields: % 46.56/15.32 | (76) ~ (all_7_0_3 = all_7_1_4) & singleton(all_7_2_5) = all_7_0_3 & unordered_pair(all_7_2_5, all_7_2_5) = all_7_1_4 % 46.56/15.32 | % 46.56/15.32 | Applying alpha-rule on (76) yields: % 46.56/15.32 | (77) ~ (all_7_0_3 = all_7_1_4) % 46.56/15.32 | (78) singleton(all_7_2_5) = all_7_0_3 % 46.56/15.32 | (79) unordered_pair(all_7_2_5, all_7_2_5) = all_7_1_4 % 46.56/15.32 | % 46.56/15.32 | Instantiating formula (55) with all_7_0_3, all_7_2_5 and discharging atoms singleton(all_7_2_5) = all_7_0_3, yields: % 46.56/15.32 | (80) in(all_7_2_5, all_7_0_3) & ! [v0] : (v0 = all_7_2_5 | ~ in(v0, all_7_0_3)) % 46.56/15.32 | % 46.56/15.32 | Applying alpha-rule on (80) yields: % 46.56/15.32 | (81) in(all_7_2_5, all_7_0_3) % 46.56/15.32 | (82) ! [v0] : (v0 = all_7_2_5 | ~ in(v0, all_7_0_3)) % 46.56/15.32 | % 46.56/15.32 | Instantiating formula (18) with all_7_1_4, all_7_2_5, all_7_2_5 and discharging atoms unordered_pair(all_7_2_5, all_7_2_5) = all_7_1_4, yields: % 46.56/15.32 | (83) in(all_7_2_5, all_7_1_4) & ! [v0] : (v0 = all_7_2_5 | ~ in(v0, all_7_1_4)) % 46.56/15.32 | % 46.56/15.32 | Applying alpha-rule on (83) yields: % 46.56/15.32 | (84) in(all_7_2_5, all_7_1_4) % 46.56/15.32 | (85) ! [v0] : (v0 = all_7_2_5 | ~ in(v0, all_7_1_4)) % 46.56/15.32 | % 46.56/15.32 | Introducing new symbol ex_78_1_20 defined by: % 46.56/15.32 | (86) ex_78_1_20 = all_7_0_3 % 46.56/15.32 | % 46.56/15.32 | Introducing new symbol ex_78_0_19 defined by: % 46.56/15.32 | (87) ex_78_0_19 = all_7_1_4 % 46.56/15.32 | % 46.56/15.32 | Instantiating formula (56) with ex_78_0_19, ex_78_1_20 yields: % 46.56/15.32 | (88) ex_78_0_19 = ex_78_1_20 | ? [v0] : (( ~ in(v0, ex_78_0_19) | ~ in(v0, ex_78_1_20)) & (in(v0, ex_78_0_19) | in(v0, ex_78_1_20))) % 46.56/15.32 | % 46.56/15.32 +-Applying beta-rule and splitting (88), into two cases. % 46.56/15.32 |-Branch one: % 46.56/15.32 | (89) ex_78_0_19 = ex_78_1_20 % 46.56/15.32 | % 46.56/15.32 | Combining equations (87,89) yields a new equation: % 46.56/15.32 | (90) ex_78_1_20 = all_7_1_4 % 46.56/15.32 | % 46.56/15.32 | Combining equations (90,86) yields a new equation: % 46.56/15.32 | (91) all_7_0_3 = all_7_1_4 % 46.56/15.32 | % 46.56/15.32 | Equations (91) can reduce 77 to: % 46.56/15.32 | (92) $false % 46.56/15.32 | % 46.56/15.32 |-The branch is then unsatisfiable % 46.56/15.32 |-Branch two: % 46.56/15.32 | (93) ? [v0] : (( ~ in(v0, ex_78_0_19) | ~ in(v0, ex_78_1_20)) & (in(v0, ex_78_0_19) | in(v0, ex_78_1_20))) % 46.56/15.32 | % 46.56/15.32 | Instantiating (93) with all_81_0_23 yields: % 46.56/15.32 | (94) ( ~ in(all_81_0_23, ex_78_0_19) | ~ in(all_81_0_23, ex_78_1_20)) & (in(all_81_0_23, ex_78_0_19) | in(all_81_0_23, ex_78_1_20)) % 46.56/15.32 | % 46.56/15.32 | Applying alpha-rule on (94) yields: % 46.56/15.32 | (95) ~ in(all_81_0_23, ex_78_0_19) | ~ in(all_81_0_23, ex_78_1_20) % 46.56/15.32 | (96) in(all_81_0_23, ex_78_0_19) | in(all_81_0_23, ex_78_1_20) % 46.56/15.32 | % 46.56/15.32 +-Applying beta-rule and splitting (95), into two cases. % 46.56/15.32 |-Branch one: % 46.56/15.32 | (97) ~ in(all_81_0_23, ex_78_0_19) % 46.56/15.32 | % 46.56/15.32 +-Applying beta-rule and splitting (96), into two cases. % 46.56/15.32 |-Branch one: % 46.56/15.32 | (98) in(all_81_0_23, ex_78_0_19) % 46.56/15.32 | % 46.56/15.32 | Using (98) and (97) yields: % 46.56/15.32 | (99) $false % 46.56/15.32 | % 46.56/15.32 |-The branch is then unsatisfiable % 46.56/15.32 |-Branch two: % 46.56/15.32 | (100) in(all_81_0_23, ex_78_1_20) % 46.56/15.32 | % 46.56/15.32 | Instantiating formula (82) with all_81_0_23 yields: % 46.56/15.32 | (101) all_81_0_23 = all_7_2_5 | ~ in(all_81_0_23, all_7_0_3) % 46.56/15.32 | % 46.56/15.32 +-Applying beta-rule and splitting (101), into two cases. % 46.56/15.32 |-Branch one: % 46.56/15.32 | (102) ~ in(all_81_0_23, all_7_0_3) % 46.56/15.32 | % 46.56/15.32 | From (86) and (100) follows: % 46.56/15.32 | (103) in(all_81_0_23, all_7_0_3) % 46.56/15.33 | % 46.56/15.33 | Using (103) and (102) yields: % 46.56/15.33 | (99) $false % 46.56/15.33 | % 46.56/15.33 |-The branch is then unsatisfiable % 46.56/15.33 |-Branch two: % 46.56/15.33 | (105) all_81_0_23 = all_7_2_5 % 46.56/15.33 | % 46.56/15.33 | From (105) and (97) follows: % 46.56/15.33 | (106) ~ in(all_7_2_5, ex_78_0_19) % 46.56/15.33 | % 46.56/15.33 | From (87) and (106) follows: % 46.56/15.33 | (107) ~ in(all_7_2_5, all_7_1_4) % 46.56/15.33 | % 46.56/15.33 | Using (84) and (107) yields: % 46.56/15.33 | (99) $false % 46.56/15.33 | % 46.56/15.33 |-The branch is then unsatisfiable % 46.56/15.33 |-Branch two: % 46.56/15.33 | (98) in(all_81_0_23, ex_78_0_19) % 46.56/15.33 | (110) ~ in(all_81_0_23, ex_78_1_20) % 46.56/15.33 | % 46.56/15.33 | Instantiating formula (82) with all_81_0_23 yields: % 46.56/15.33 | (101) all_81_0_23 = all_7_2_5 | ~ in(all_81_0_23, all_7_0_3) % 46.56/15.33 | % 46.56/15.33 | Instantiating formula (85) with all_81_0_23 yields: % 46.56/15.33 | (112) all_81_0_23 = all_7_2_5 | ~ in(all_81_0_23, all_7_1_4) % 46.56/15.33 | % 46.56/15.33 +-Applying beta-rule and splitting (101), into two cases. % 46.56/15.33 |-Branch one: % 46.56/15.33 | (102) ~ in(all_81_0_23, all_7_0_3) % 46.56/15.33 | % 46.56/15.33 +-Applying beta-rule and splitting (112), into two cases. % 46.56/15.33 |-Branch one: % 46.56/15.33 | (114) ~ in(all_81_0_23, all_7_1_4) % 46.56/15.33 | % 46.56/15.33 | From (87) and (98) follows: % 46.56/15.33 | (115) in(all_81_0_23, all_7_1_4) % 46.56/15.33 | % 46.56/15.33 | Using (115) and (114) yields: % 46.56/15.33 | (99) $false % 46.56/15.33 | % 46.56/15.33 |-The branch is then unsatisfiable % 46.56/15.33 |-Branch two: % 46.56/15.33 | (105) all_81_0_23 = all_7_2_5 % 46.56/15.33 | % 46.56/15.33 | From (105) and (102) follows: % 46.56/15.33 | (118) ~ in(all_7_2_5, all_7_0_3) % 46.56/15.33 | % 46.56/15.33 | Using (81) and (118) yields: % 46.56/15.33 | (99) $false % 46.56/15.33 | % 46.56/15.33 |-The branch is then unsatisfiable % 46.56/15.33 |-Branch two: % 46.56/15.33 | (105) all_81_0_23 = all_7_2_5 % 46.56/15.33 | % 46.56/15.33 | From (105) and (110) follows: % 46.56/15.33 | (121) ~ in(all_7_2_5, ex_78_1_20) % 46.56/15.33 | % 46.56/15.33 | From (86) and (121) follows: % 46.56/15.33 | (118) ~ in(all_7_2_5, all_7_0_3) % 46.56/15.33 | % 46.56/15.33 | Using (81) and (118) yields: % 46.56/15.33 | (99) $false % 46.56/15.33 | % 46.56/15.33 |-The branch is then unsatisfiable % 46.56/15.33 % SZS output end Proof for theBenchmark % 46.56/15.33 % 46.56/15.33 14675ms %------------------------------------------------------------------------------